GEOPLEX: GSSA and VSS models

Abstract

This report describes some aspects of the theory of Variable Structure Systems (VSS). It starts with the state-of-the-art classical methods of control and evolves to a description based on average port Hamiltonian models. In the framework of GEOPLEX, VSS appears due to the fact that some of the plants of interest are controlled using power converters, which are systems, changing between several circuits topologies. In section 2, the basic ideas of Sliding Mode Control (SMC) for VSS are presented, and a somewhat detailed exposition of its application to the control of a power converter is given. Most of section 3 is unpublished material, describing some preliminary results about the relation between (generalized) averaging and the port Hamiltonian description. The fundamentals of State Space Averaging (SSA) and Generalized Space State Averaging (GSSA) are presented, and averaged port Hamiltonian models for second order power converters are introduced. There is a summary of some rigorous mathematical results about GSSA, and a relationship between the Hamiltonians of the GSSA models and the original Hamiltonian is established for systems with quadratic Hamiltonian functions.